Norm closure of classical pseudodifferential operators does not contain Hörmander's class

Details Norm closure of classical pseudodifferential operators does not contain Hörmander's class Norm closure of classical pseudodifferential operators does not contain Hörmander's class

2003-12-12

arxiv.org/abs/math/0312261v1

Mathematics

Operator Algebras

Scientific paper

The L2-norm closure of the algebra of all zero-order classical (or
polyhomogeneous) pseudodifferential operators on a closed manifold $X$ is
proven not to contain H\"ormander's class $\Psi^0(X)$. A set of generators (for
that closed algebra) smaller than all zero-order classical pseudos is also
described.

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